1. Field of the Invention
The present invention relates to a controller for feedback-controlling a controlled system by PI or PID (P: proportional, I: integral, D: derivative) operations and, more particularly, to a two degrees of freedom controller for realizing two degrees of freedom (2DOF) control for simultaneously optimizing a process-disturbance control characteristic and a setpoint-following characteristic using functional blocks having a mimimum time element.
2. Description of the Related Art
A conventional 2DOF PI controller is disclosed in U.S. Pat. No. 4,755,924, and has a setpoint filter 1 which follows a change in setpoint value, as shown in FIG. 1, thereby performing 2DOF PI control. More specifically, the setpoint filter 1 receives a setpoint value SV, executes calculation processing for 2DOF-controlling a proportional gain and an integral time, and outputs a control setpoint value SV.sub.0. The control setpoint value SV.sub.0 obtained from the setpoint filter 1 and a control value PV from a controlled system 2 are supplied to a deviation-calculating means 3, and are subjected to a calculation (SV.sub.0 -PV), thereby obtaining a deviation E. Thereafter, the deviation E is supplied to a PI control operation means 4 expressed by a transfer function K.sub.p { 1+1/(T.sub.I .multidot.S)} (where K.sub.P is the proportional gain, T.sub.I is the integral time, and S is the Laplace operator). The PI control operation means 4 executes a PI control operation on the basis of the transfer function, and a calculated manipulative variable MV is supplied to an addition means 5. The manipulative variable MV and a disturbance signal D are added to each other by the means 5, and the sum is applied to the controlled system 2 to control the system 2 so that the setpoint value SV.sub.0 =the control value PV.
The setpoint filter 1 comprises a lead/lag means 1.sub.1, a 1st lag means 1.sub.2, an incomplete derivative means 1.sub.3, and a subtraction means 1.sub.4. The lead/lag means 1.sub.1 has a function of adjusting a compensation timing by a desired lead or lag time in consideration of a process time constant upon reception of the setpoint value SV. The 1st lag means 1.sub.2 has a function of providing a 1st lag upon reception of the setpoint value SV. The incomplete derivative means 1.sub.3 performs an incomplete derivative upon reception of an output from the 1st lag means 1.sub.2. The subtraction means 1.sub.4 subtracts an output from the incomplete derivative means 1.sub.3 from an output from the lead/lag means 1.sub.1.
Therefore, according to this arrangement of the setpoint filter 1, a transfer function CP.sub.V (S) between PV.fwdarw.MV is given by: ##EQU2## On the other hand, a transfer function C.sub.SV (S) between SV.fwdarw.MV is given by: ##EQU3## where .alpha. is a 2DOF coefficient (a constant which can be set between 0 and 1) of the proportional gain, and .beta..sub.0 is a 2DOF coefficient (a constant which can be set between 0 and 1) of the integral time. Therefore, after K.sub.p and T.sub.I are determined to optimize a process-disturbance control characteristic from the above equations, .alpha. and .beta..sub.0 can be determined to optimize a setpoint-following characteristic, thus realizing 2DOF control.
FIG. 2 is a diagram showing an arrangement of a conventional 2DOF PID controller disclosed in U.S. Pat. No. 4,755,924. This controller has a setpoint filter 10 which follows a change in setpoint value, and performs complete 2DOF PID control associated with PID. More specifically, the setpoint filter 10 receives a setpoint value SV, and performs calculation processing for realizing complete 2DOF-control of three terms, i.e., a proportional gain K.sub.p, an integral time T.sub.I, and a derivative time T.sub.D, thereby outputting a control setpoint value SV.sub.0. The control setpoint value SV.sub.0 obtained from the setpoint filter 10, and a control value PV from a controlled system 2 are supplied to a deviation-calculating means 3, and are subjected to a calculation (SV.sub.0 -PV), thereby obtaining a deviation E. The deviation E is supplied to a PI control operation means 4 expressed by a transfer function K.sub.P {1+1/(T.sub.I .multidot.S)} (where K.sub.P is the proportional gain, T.sub.I is the integral time, and S is the Laplace operator) via a nonlinear processing means 6. The PI control operation means 4 executes a PI control operation on the basis of the transfer function, and a calculated manipulative variable MV is supplied to a subtraction means 7. The subtraction means 7 subtracts the output from an incomplete derivative means 8 for performing an incomplete derivative on the basis of the control value PV from the manipulative variable MV, and a calculated difference signal is supplied to an addition means 5. The addition means 5 adds the output signal from the subtraction means 7 and a disturbance signal D, and the sum signal is applied to the controlled system 2. Thus, the system 2 is controlled so that the setpoint value SV.sub.0 =the control value PV.
The setpoint filter 10 comprises a lead/lag means 10.sub.1, a 1st lag means 10.sub.2, an incomplete derivative means 10.sub.3, and an incomplete derivative means 10.sub.4, which have the similar functions as those in the setpoint filter 1.
The incomplete derivative means 10.sub.4 is adopted to realize 2DOF control, and is expressed by a transfer function {(.gamma.T.sub.D .multidot.S)/(1+.eta.T.sub.D .multidot.S)}. Furthermore, the filter 10 comprises a subtraction means 10.sub.5, so that the output from the 1st lag means 10.sub.2 is subtracted from the output from the incomplete derivative means 10.sub.4. The difference is supplied to the incomplete derivative means 10.sub.3. The output from the incomplete derivative means 10.sub.3 and the output from the lead/lag means 10.sub.1 are added to each other by an addition means 10.sub.6, thus obtaining the control setpoint value SV.sub.0.
Therefore, a transfer function C.sub.PV (S) between PV.fwdarw.MV of the setpoint filter 10 is given by: ##EQU4## On the other hand, a transfer function C.sub.SV (S) between SV.fwdarw.MV is given by: ##EQU5## where .eta. is a constant which can be set between 0.1 and 1, .alpha. is a 2DOF coefficient (a constant which can be set between 0 and 1) of the proportional gain, .beta..sub.0 is a 2DOF coefficient (a constant which can be set between 0 and 1) of the integral time, and .gamma. is a 2DOF coefficient (a constant which can be set between 0 and 2) of the derivative time.
Therefore, after K.sub.p, T.sub.I, and T.sub.D are determined to optimize a process-disturbance control characteristic on the basis of equations (3) and (4), .alpha., .beta..sub.0, and .gamma. can be determined to optimize a setpoint-following characteristic, thus realizing 2DOF PID control.
However, although the above-mentioned PI or PID controller has various features, the following problems are pointed out.
1 There are three or more functional blocks associated with time, which are added to realize 2DOF control. Therefore, the entire plant instrumentation system requires a vary large number of functional blocks.
In general, a large number of PID control loops are used in a plant instrumentation system. Therefore, if at least one functional block can be eliminated per PID control loop, a system load can be greatly reduced, and an operation speed can be increased accordingly. In other words, when PI or PID 2DOF control is realized using a smaller number of functional blocks, practical merits are considerable.
2 An optimal value of the 2DOF coefficient .beta..sub.0 of the integral time largely depends on the magnitude of L/T (L: idling time, T: time constant) of a controlled system.
More specifically, the value of the 2DOF coefficient .alpha. of the proportional gain can be specified by CHR (Chien Hrones Reswick) or the like in a PID parameter optimizing control method. However, the value of the 2DOF coefficient .beta..sub.0 of the integral time cannot be specified, and must be specified by trials and errors in units of characteristics of controlled systems 2. However, since the 2DOF coefficient .beta..sub.0 of the integral time has a high gain, a process characteristic is considerably changed when the gain of .beta..sub.0 is controlled. Therefore, it is difficult to attain fine tuning, resulting in cumbersome control.
3 The role of 2DOF control of the setpoint filter is not clear.
In general, several tens to several thousands of PID control loops are distributed in a single plant instrumentation system. Therefore, if their roles are clarified, the control loops are industrially useful. When analysis of an abnormality is performed, or when the loops are applied to various modifications, a simple functional arrangement is indispensable. However, in the existing PID control loop, the role of the 2DOF control of the setpoint filter is not clear. Nonlinear processing is inaccurate.
4 Nonlinear processing is inaccurate.
In the conventional PID controller, a control value PV is supplied to the incomplete derivative means 8, and an incomplete derivative output from the incomplete derivative means 8 is supplied to the output side of the PI control operation means 4. Therefore, the incomplete derivative output bypasses the nonlinear processing means 6 to which the deviation E is input. As a result, nonlinear processing cannot be accurately, simply, and desirably executed, and controllability is limited.
Therefore, in order to completely transit from 1DOF PID to 2DOF PID, it is very important to perfectly overcome the above-mentioned problems.